Q: What are the factor combinations of the number 589,345?

 A:
Positive:   1 x 5893455 x 117869311 x 1895379 x 1555
Negative: -1 x -589345-5 x -117869-311 x -1895-379 x -1555


How do I find the factor combinations of the number 589,345?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 589,345, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 589,345
-1 -589,345

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 589,345.

Example:
1 x 589,345 = 589,345
and
-1 x -589,345 = 589,345
Notice both answers equal 589,345

With that explanation out of the way, let's continue. Next, we take the number 589,345 and divide it by 2:

589,345 ÷ 2 = 294,672.5

If the quotient is a whole number, then 2 and 294,672.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 589,345
-1 -589,345

Now, we try dividing 589,345 by 3:

589,345 ÷ 3 = 196,448.3333

If the quotient is a whole number, then 3 and 196,448.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 589,345
-1 -589,345

Let's try dividing by 4:

589,345 ÷ 4 = 147,336.25

If the quotient is a whole number, then 4 and 147,336.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 589,345
-1 589,345
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

153113791,5551,895117,869589,345
-1-5-311-379-1,555-1,895-117,869-589,345

More Examples

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